Problem: Solve for $x$ : $x^2 - 2x - 24 = 0$
Answer: The coefficient on the $x$ term is $-2$ and the constant term is $-24$ , so we need to find two numbers that add up to $-2$ and multiply to $-24$ The two numbers $-6$ and $4$ satisfy both conditions: $ {-6} + {4} = {-2} $ $ {-6} \times {4} = {-24} $ $(x {-6}) (x + {4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -6) (x + 4) = 0$ $x - 6 = 0$ or $x + 4 = 0$ Thus, $x = 6$ and $x = -4$ are the solutions.